Dopo cena, facciamo una passeggiata lungo il fiume.

In Italian, meals are often used without an article when you mean them in a general, everyday sense:

• dopo cena = after dinner
• prima di pranzo = before lunch
• a colazione = at breakfast

If you say dopo la cena, it usually sounds more specific, as in after the dinner / after that particular dinner. In your sentence, dopo cena just means after dinner in a normal, routine sense.

Yes, facciamo literally comes from fare and often means we do or we make, but Italian uses fare una passeggiata as a fixed expression meaning to take a walk.

So:

• fare una passeggiata = to take a walk
• facciamo una passeggiata = we take a walk / let’s take a walk

This is very common in Italian. Similar patterns include:

• fare una foto = to take a photo
• fare colazione = to have breakfast
• fare una pausa = to take a break

It can mean both, depending on context.

• facciamo una passeggiata can mean we take a walk
• but very often, especially in conversation, it can also mean let’s take a walk

Italian often uses the 1st person plural present tense this way to make suggestions:

• Andiamo? = Shall we go? / Let’s go.
• Mangiamo fuori. = Let’s eat out.
• Facciamo una passeggiata. = Let’s take a walk.

Without more context, both readings are possible.

Italian usually does not need subject pronouns because the verb ending already shows who the subject is.

Here, facciamo clearly means we do / we make / let’s do, so noi is unnecessary.

• Facciamo una passeggiata. = We take a walk / Let’s take a walk.
• Noi facciamo una passeggiata. = We take a walk.

Adding noi is possible, but it usually gives emphasis, contrast, or clarification:

• Noi facciamo una passeggiata, loro restano a casa.
  We are taking a walk; they are staying home.

Passeggiata means walk or stroll, usually with the idea of something pleasant, relaxed, and unhurried.

So una passeggiata is not just any movement on foot; it often suggests a leisurely walk.

Compare:

• fare una passeggiata = to take a stroll / go for a walk
• camminare = to walk

Camminare focuses more on the action of walking itself, while fare una passeggiata often sounds more like an enjoyable outing.

Italian normally uses the noun with an article in this expression:

• fare una passeggiata = to take a walk

That is simply the natural Italian structure. Even if English sometimes avoids a direct equivalent article in idiomatic translations, Italian needs it here.

So:

• facciamo una passeggiata = natural
• facciamo passeggiata = incorrect

Lungo il fiume means along the river.

Here:

• lungo = along
• il fiume = the river

It describes the route or location of the walk: the walk takes place along the riverbank / following the river.

This is different from:

• vicino al fiume = near the river
• sul fiume = on the river
• al fiume = at the river

So lungo il fiume specifically gives the idea of moving alongside it.

It can be both.

In this sentence, lungo is a preposition meaning along:

• lungo il fiume = along the river

But lungo can also be an adjective meaning long:

• un film lungo = a long film
• una strada lunga = a long road

So the meaning depends on how it is used in the sentence.

Italian uses articles more regularly than English in many cases. Here, il fiume is the normal way to say the river.

After a preposition like lungo, Italian still keeps the definite article when needed:

• lungo il fiume = along the river
• vicino alla casa = near the house
• dietro la scuola = behind the school

So lungo fiume would not be correct here.

Yes, that is grammatically fine, but it is a bit different in style and nuance.

• Dopo cena, facciamo una passeggiata lungo il fiume.
  More direct, compact, and idiomatic.
• Dopo la cena, andiamo a fare una passeggiata lungo il fiume.
  More explicit: After dinner, we go take a walk along the river.

Also, dopo la cena sounds more specific than dopo cena. In many everyday situations, dopo cena is the more natural choice.

Yes. Italian word order is flexible, especially with time expressions.

You can say:

• Dopo cena, facciamo una passeggiata lungo il fiume.
• Facciamo una passeggiata lungo il fiume dopo cena.

Both are correct. Putting dopo cena first gives it a little more prominence, as the time frame is introduced right away.

Facciamo is the present indicative, first person plural, of fare.

Conjugation of fare in the present:

• io faccio
• tu fai
• lui/lei fa
• noi facciamo
• voi fate
• loro fanno

Even though it is formally present tense, it can also express a suggestion, especially in context:

• Facciamo una passeggiata? = Shall we take a walk?
• Dopo cena, facciamo una passeggiata. = After dinner, we’ll take a walk / let’s take a walk.

Yes. Fare is an irregular verb.

A learner might expect something more regular, but fare behaves unusually:

• faccio
• fai
• fa
• facciamo
• fate
• fanno

The -cci- in facciamo is part of the irregular pattern of the verb. It is just something to memorize through exposure and practice.

Usually it means a literal walk or stroll, but like many words, it can be used figuratively in some contexts. Still, in a sentence like this one, the meaning is straightforward: a real walk along the river.

For a learner, the main thing to remember is the common expression:

• fare una passeggiata = to take a walk

That is the most useful and natural interpretation here.